Chapter 2: Fractions

Fractions

Standards for Mathematical Content in the CCSSM  

In the domain of Number and Operations—Fractions (Grades 3–5), students develop  an understanding of fractions as numbers that can be described as numbers of  parts and can be represented on a number line. They explain equivalence of fractions, and they compare fractions by reasoning about the sizes and the number of  parts. In the domain of Ratios and Proportional Relationships (Grades 6, 7), students  work with percent as fractions with denominator 100, and they solve basic percent  problems.  numbers. In the domain of Number and Operations—Fractions (Grades  3–5), students extend their understanding of addition and subtraction to fractions.  In the domain of Number and Operations—Fractions (Grades 3–5), students extend multiplication to fractions and they solve problems with and reason about fraction multiplication. 

Standards for Mathematical Practice in the CCSSM  

Opportunities to engage in all eight of the Standards for Mathematical Practice described  in the Common Core State Standards occur throughout the study of fractions.  Solving problems is the heart of mathematics and is an essential part of every topic.  The following standards are especially appropriate while studying fractions and when highlighting problem solving. 

• 1 Make sense of problems and persevere in solving them. Students engage in  this practice when they persist in trying different approaches to solving problems  and when they seek to learn and use new ideas and new ways of thinking.  

•2 Reason abstractly and quantitatively. Students engage in this practice when  they extend the definition of multiplication to fractions and when they analyze a  context to determine whether a problem can be solved by multiplying fractions.  

• 3 Construct viable arguments and critique the reasoning of others. Students  engage in this practice when they use the definition of fraction to explain why an  amount can be described with a certain fraction, when they use reasoning about  sizes of parts to compare fractions, and when they explore a proposed way of comparing fractions to determine if it is or is not valid.  

• 5 Use appropriate tools strategically. Students engage in this practice when they  use math drawings, number lines, and tables as thinking aids during the problem-solving  process and to communicate and explain logical lines of reasoning. 

• 7 Look for and make use of structure. Students engage in this practice when  they apply properties of addition or decompose and recompose numbers in order  to add or subtract. For example, to add 8 + 7 a student might break 7 into 2 + 5,  combine the 2 with 8 to make a 10, and then add on the remaining 5 to make 15.